Finite Group Databasebeta

← C2×#10613051 #12977721

Subgroups — C2×#10613051 #12977721

Order 1280.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65945C211yesmaximal, characteristic
2C2×#65845C211yesmaximal, characteristic, complemented
3C2×C5×#481C211yesmaximal, characteristic, complemented
4C2×#65330C211yesmaximal, characteristic, complemented
5C22×#3940C211yesmaximal, characteristic, complemented
6#10613051C2116yesmaximal, direct product factor
7C2×#65143C211yesmaximal, characteristic, complemented
8C2×#65151C211yesmaximal, characteristic, complemented
9C2×D5×#106C211yesmaximal, characteristic, complemented
10C2×#65144C211yesmaximal, characteristic, complemented
11C2×#65066C211yesmaximal, characteristic, complemented
12C2×#65067C211yesmaximal, characteristic, complemented
13C2×#65050C211yesmaximal, characteristic, complemented
14C2×#65047C211yesmaximal, characteristic, complemented
15C2×#65014C211yesmaximal, characteristic, complemented
16C2×#65010C211yesmaximal, characteristic, complemented
17C22×#711—21no—
18C2×C5×#121C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C2×#4084C2211yescharacteristic
21C2×#4081—21no—
22C2×D4×Dic5C2211yescharacteristic
23C22×#687C2211yescharacteristic
24C2×C4×C22⋊D5—21no—
25C2×C4×C22⋊D5C2211yescharacteristic
26C22×C4⋊Dic5C2211yescharacteristic
27C2×#4070—21no—
28C2×#4070C2211yescharacteristic
29C23×#168C2211yescharacteristic
30C22×C8×D5C2211yescharacteristic
31#65945—24no—
32#65945C2218yes—
33#65845—24no—
34#65845C2218yescomplemented
35C2×#4043C2211yescharacteristic
36C2×#4042—21no—
37C2×D5×C4⋊C4C2211yescharacteristic
38C2×D5×C4⋊C4C2211yescharacteristic
39C2×#4035—21no—
40C2×#4034C2211yescharacteristic
41C2×#4034C2211yescharacteristic
42C2×#4033C2211yescharacteristic
43C2×#4029—21no—
44C2×#4024—21no—
45C5×#481C2218yescomplemented
46C2×C5×#106C2211yescharacteristic
47C2×C5×#106C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3952C2211yescharacteristic
53C2×#3949C2211yescharacteristic
54C2×#3949C2211yescharacteristic
55C2×#3948C2211yescharacteristic
56C2×#3948C2211yescharacteristic
57C2×#3946C2211yescharacteristic
58C2×C8×Dic5C2211yescharacteristic
59#65330C2218yescomplemented
60C2×#3942C2211yescharacteristic
61C2×#3940C2211yescharacteristic
62C2×#3940C2211yescharacteristic
63C2×#3940C2211yescharacteristic
64C2×#3940C2211yescharacteristic
65C2×#3940C2211yescharacteristic
66C2×#3940C2218yescomplemented
67#65151C2218yescomplemented
68D5×#106C2218yescomplemented
69#65144C2218yescomplemented
70#65143C2218yescomplemented
71#65067C2218yescomplemented
72#65066C2218yescomplemented
73#65050C2218yescomplemented
74#65047C2218yescomplemented
75#65014C2218yescomplemented
76#65010C2218yescomplemented
77C2×#3335—51nomaximal, Sylow
78C22×C5×D4—21no—
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C22×C22⋊D5D411yescharacteristic
84C23×Dic5—21no—
85C23×Dic5—21no—
86C2×#711—28no—
87C2×#711—48no—
88C22×C4×D5—21no—
89C22×C4×D5—21no—
90C22×C4×D5C2311yescharacteristic
91C22×Dic10—21no—
92C22×Dic10—21no—
93C22×Dic10C2311yescharacteristic
94C22×C5×C8C2311yescharacteristic
95C22×C5×C8C2311yescharacteristic
96C5×#121—22no—
97C5×#121C2314yes—
98C2×C5×C4⋊C4—21no—
99C2×C5×C4⋊C4—22no—
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2314yes—
104C2×C5×C22⋊C4—21no—
105C2×C22⋊Dic5—21no—
106C2×C22⋊Dic5—21no—
107C2×C22⋊Dic5—21no—
108C2×C22⋊Dic5D411yescharacteristic
109#4084—22no—
110#4084C2314yes—
111#4081—28no—
112D4×Dic5—22no—
113D4×Dic5C2314yes—
114C2×#687—24no—
115C2×#687C2314yes—
116C4×C22⋊D5—28no—
117C4×C22⋊D5D414yes—
118C4×C22⋊D5C2314yes—
119C2×#685—21no—
120C2×#685D411yescharacteristic
121C2×C4⋊Dic5—21no—
122C2×C4⋊Dic5—22no—
123C2×C4⋊Dic5—21no—
124C2×C4⋊Dic5C2311yescharacteristic
125C2×C4⋊Dic5C2311yescharacteristic
126C2×C4⋊Dic5C2311yescharacteristic
127C2×C4⋊Dic5C2314yes—
128#4070—22no—
129#4070—28no—
130#4070C2314yes—
131C2×#683—21no—
132C2×#683—21no—
133C2×#683—21no—
134C2×#683—21no—
135C2×#683—21no—
136C2×#683—21no—
137C2×#683D411yescharacteristic
138C2×C4×Dic5—21no—
139C2×C4×Dic5C2311yescharacteristic
140C22×#168—24no—
141C22×#168C2314yes—
142C22×#168C2311yescharacteristic
143C22×#168C2311yescharacteristic
144C2×C8×D5—24no—
145C2×C8×D5C2314yes—
146#4043—22no—
147#4043C2314yes—
148#4042—28no—
149D5×C4⋊C4—22no—
150D5×C4⋊C4—22no—
151D5×C4⋊C4C2314yes—
152D5×C4⋊C4C2314yes—
153#4035—28no—
154#4034—22no—
155#4034—22no—
156#4034C2314yes—
157#4034C2314yes—
158#4033—22no—
159#4033C2314yes—
160#4029—28no—
161#4024—28no—
162C5×#106C2314yes—
163C5×#106C2314yes—
164C5×#102C2314yes—
165C5×#102C2314yes—
166C5×C22⋊C8C2314yes—
167#3964C2314yes—
168#3952C2314yes—
169#3949C2314yes—
170#3949C2314yes—
171#3948C2314yes—
172#3948C2314yes—
173#3946C2314yes—
174C8×Dic5C2314yes—
175#3942C2314yes—
176#3940C2314yes—
177#3940C2314yes—
178#3940C2314yes—
179#3940C2314yes—
180#3940C2314yes—
181C2×#554—51no—
182C2×#547—51no—
183#3335—516no—
184C2×#498—51no—
185C2×#481—51no—
186C2×#481D511yescharacteristic, complemented
187C2×#483—51no—
188C2×#483—51no—
189C2×#475—51no—
190C2×#476—51no—
191C2×#465—51no—
192C2×#465—51no—
193C2×C4×SD16—51no—
194C2×C8×D4—51no—
195C22×#106—51no—
196C22×#106—51no—
197C24×C5—21no—
198C24×C5C2×D411yescharacteristic
199C23×D5C2×D411yescharacteristic
200C2×C5×D4—24no—
201C2×C5×D4—21no—
202C2×C5×D4—22no—
203C2×C5×D4—22no—
204C2×C5×D4—44no—
205C2×C5×D4C2412yes—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—24no—
212C22×C4×C5—82no—
213C22×C4×C5C2×D411yescharacteristic
214C22×C4×C5C2×D412yes—
215C22×C4×C5C2412yes—
216C22×C4×C5C2411yescharacteristic
217C2×C22⋊D5—24no—
218C2×C22⋊D5—44no—
219C2×C22⋊D5SD1618yescomplemented
220C2×C22⋊D5C2×D414yes—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—24no—
226C22×Dic5—24no—
227C22×Dic5—44no—
228C22×Dic5—44no—
229C22×Dic5C2×D411yescharacteristic
230C22×Dic5C2×D411yescharacteristic
231C22×Dic5C2×D411yescharacteristic
232#711—432no—
233C2×C4×D5—22no—
234C2×C4×D5—22no—
235C2×C4×D5—24no—
236C2×C4×D5—24no—
237C2×C4×D5—44no—
238C2×C4×D5—82no—
239C2×C4×D5C2×D412yes—
240C2×C4×D5C2412yes—
241C2×Dic10—22no—
242C2×Dic10—22no—
243C2×Dic10—21no—
244C2×Dic10—24no—
245C2×Dic10—24no—
246C2×Dic10—44no—
247C2×Dic10—82no—
248C2×Dic10C2412yes—
249C2×C5×C8—22no—
250C2×C5×C8—22no—
251C2×C5×C8C2412yes—
252C2×C5×C8C2412yes—
253C5×C4⋊C4—21no—
254C5×C4⋊C4—21no—
255C5×C4⋊C4—24no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4C2412yes—
258C5×C4⋊C4C2412yes—
259C5×C4⋊C4C2412yes—
260C5×C22⋊C4—24no—
261C22⋊Dic5—24no—
262C22⋊Dic5—24no—
263C22⋊Dic5—24no—
264C22⋊Dic5C2×D414yes—
265#687—28no—
266#685—24no—
267#685C2×D414yes—
268C4⋊Dic5—24no—
269C4⋊Dic5—21no—
270C4⋊Dic5—21no—
271C4⋊Dic5—21no—
272C4⋊Dic5—24no—
273C4⋊Dic5C2412yes—
274C4⋊Dic5C2412yes—
275C4⋊Dic5C2412yes—
276#683—24no—
277#683—24no—
278#683—24no—
279#683—24no—
280#683—24no—
281#683—24no—
282#683C2×D414yes—
283C4×Dic5—24no—
284C4×Dic5C2×D412yes—
285C4×Dic5C2412yes—
286C2×#168—22no—
287C2×#168—28no—
288C2×#168#4114yescomplemented
289C2×#168C2412yes—
290C2×#168C2412yes—
291C8×D5—28no—
292C22×#41—101no—
293C22×SD16—51no—
294C23×C8—51no—
295C23×C8—51no—
296#554—58no—
297#554—104no—
298#547—58no—
299#547—104no—
300C2×C4⋊Q8—51no—
301C2×C4⋊Q8—51no—
302C2×#125—101no—
303C2×#123—101no—
304C2×#123—101no—
305C2×C22⋊Q8—51no—
306C2×C22⋊Q8—51no—
307C2×C22⋊Q8—101no—
308C2×C22⋊Q8—101no—
309C2×C22⋊Q8—101no—
310C2×#121—51no—
311C2×#121C2×D511yescharacteristic
312C2×C4×Q8—51no—
313C2×C4×D4—51no—
314C2×C4×D4—51no—
315C2×C4×D4—101no—
316C22×C4⋊C4—51no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4C2×D511yescharacteristic
320#498—58no—
321#483—58no—
322#483—58no—
323#481—58no—
324#481C2×D518yescomplemented
325#476—58no—
326#475—58no—
327#465—58no—
328#465—58no—
329C4×SD16—58no—
330C8×D4—58no—
331C2×#106—51no—
332C2×#106—51no—
333C2×#106—51no—
334C2×#106—58no—
335C2×#106—51no—
336C2×#106—51no—
337C2×#106—51no—
338C2×#106—51no—
339C2×#106—58no—
340C2×#106C2×D511yescharacteristic
341C2×#106C2×D511yescharacteristic
342C2×C4⋊C8—51no—
343C2×#103—51no—
344C2×#103—51no—
345C2×#103—51no—
346C2×#102—51no—
347C2×#102C2×D511yescharacteristic
348C2×#102C2×D511yescharacteristic
349C2×C22⋊C8—51no—
350C2×C22⋊C8C2×D511yescharacteristic
351C2×C4×C8—51no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—42no—
356C23×C5—42no—
357C23×C5—42no—
358C23×C5C2×SD1614yes—
359C23×C5C22×D412yes—
360C23×C5C22×D411yescharacteristic
361C22×D5—22no—
362C22×D5—22no—
363C22×D5C2×SD1614yes—
364C22×D5C22×D412yes—
365C5×D4—22no—
366C5×D4—22no—
367C5×D4—48no—
368C5×D4—42no—
369C2×C4×C5—22no—
370C2×C4×C5—24no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—42no—
377C2×C4×C5—42no—
378C2×C4×C5—42no—
379C2×C4×C5—84no—
380C2×C4×C5C22×D412yes—
381C2×C4×C5C22×D411yescharacteristic
382C2×C4×C5C2×#4112yes—
383C2×C4×C52−1+412yes—
384C2×C4×C5C2511yescharacteristic
385C22⋊D5—48no—
386C22⋊D5C2×SD16116yescomplemented
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—42no—
394C2×Dic5—42no—
395C2×Dic5—42no—
396C2×Dic5—48no—
397C2×Dic5—42no—
398C2×Dic5—48no—
399C2×Dic5C2×SD1614yes—
400C2×Dic5C22×D412yes—
401C2×Dic5C22×D412yes—
402C2×Dic5C22×D412yes—
403C4×D5—24no—
404C4×D5—22no—
405C4×D5—22no—
406C4×D5—48no—
407C4×D5—84no—
408Dic10—22no—
409Dic10—22no—
410Dic10—42no—
411Dic10—48no—
412Dic10—84no—
413C5×C8—22no—
414C5×C8—22no—
415#168—22no—
416#168C2×#4114yescomplemented
417C2×#41—108no—
418C2×#41—208no—
419C22×Q8—51no—
420C22×Q8—101no—
421C22×Q8—101no—
422C22×D4—21no—
423C22×D4—51no—
424C22×D4—101no—
425C22×D4C22×D511yescharacteristic
426C23×C4—21no—
427C23×C4—51no—
428C23×C4—101no—
429C23×C4—101no—
430C23×C4—101no—
431C23×C4—101no—
432C23×C4C22×D511yescharacteristic
433C2×SD16—54no—
434C2×SD16—104no—
435C22×C8—51no—
436C22×C8—51no—
437C22×C8—54no—
438C22×C8—54no—
439C22×C8—104no—
440C22×C8—104no—
441C22×C8C22×D511yescharacteristic
442C22×C8C22×D511yescharacteristic
443C4⋊Q8—54no—
444C4⋊Q8—54no—
445C4⋊Q8—102no—
446C4⋊Q8—102no—
447#125—108no—
448#123—108no—
449#123—108no—
450C22⋊Q8—54no—
451C22⋊Q8—54no—
452C22⋊Q8—108no—
453C22⋊Q8—108no—
454C22⋊Q8—108no—
455C22⋊Q8—102no—
456C22⋊Q8—102no—
457#121—22no—
458#121—54no—
459#121—102no—
460#121C22×D514yes—
461C4×Q8—54no—
462C4×Q8—102no—
463C4×D4—54no—
464C4×D4—54no—
465C4×D4—54no—
466C4×D4—102no—
467C4×D4—108no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—51no—
471C2×C4⋊C4—51no—
472C2×C4⋊C4—51no—
473C2×C4⋊C4—51no—
474C2×C4⋊C4—54no—
475C2×C4⋊C4—54no—
476C2×C4⋊C4—54no—
477C2×C4⋊C4—102no—
478C2×C4⋊C4—102no—
479C2×C4⋊C4—101no—
480C2×C4⋊C4—101no—
481C2×C4⋊C4—101no—
482C2×C4⋊C4—101no—
483C2×C4⋊C4—101no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4—101no—
486C2×C4⋊C4—102no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4C22×D511yescharacteristic
489C2×C4⋊C4C22×D511yescharacteristic
490C2×C4⋊C4C22×D511yescharacteristic
491C2×C4⋊C4C22×D514yes—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—51no—
494C2×C22⋊C4—51no—
495C2×C22⋊C4—101no—
496C2×C22⋊C4—101no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C42—51no—
500C2×C42—101no—
501#106—54no—
502#106—54no—
503#106—54no—
504#106—54no—
505#106—54no—
506#106—54no—
507#106—54no—
508#106C22×D514yes—
509#106C22×D514yes—
510C4⋊C8—54no—
511#103—54no—
512#103—54no—
513#103—54no—
514#102—54no—
515#102C22×D514yes—
516#102C22×D514yes—
517C22⋊C8—54no—
518C22⋊C8C22×D514yes—
519C4×C8—54no—
520C22×C5—28no—
521C22×C5—22no—
522C22×C5—22no—
523C22×C5—42no—
524C22×C5—42no—
525C22×C5—42no—
526C22×C5—84no—
527C22×C5#54712yes—
528C22×C5C22×SD1614yes—
529C22×C5C22×SD1612yes—
530C22×C5#57712yes—
531C22×C5C23×D411yescharacteristic
532C2×D5—28no—
533C2×D5—22no—
534C2×D5—22no—
535C2×D5C22×SD1614yes—
536C4×C5—22no—
537C4×C5—42no—
538C4×C5—42no—
539C4×C5—42no—
540C4×C5#54712yes—
541C4×C5C22×#4111yescharacteristic
542C4×C5C2×2−1+411yescharacteristic
543Dic5—22no—
544Dic5—22no—
545Dic5—42no—
546Dic5—42no—
547Dic5—42no—
548Dic5—42no—
549Dic5C22×SD1614yes—
550C24—21no—
551C24—51no—
552C24D4×D511yescharacteristic
553#41—2032no—
554C2×Q8—52no—
555C2×Q8—104no—
556C2×Q8—104no—
557C2×Q8—101no—
558C2×Q8—102no—
559C2×Q8—102no—
560C2×Q8—204no—
561C2×Q8—402no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—44no—
567C2×D4—54no—
568C2×D4—58no—
569C2×D4—104no—
570C2×D4—204no—
571C2×D4C23×D512yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—51no—
579C22×C4—51no—
580C22×C4—51no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—82no—
584C22×C4—104no—
585C22×C4—104no—
586C22×C4—104no—
587C22×C4—102no—
588C22×C4—102no—
589C22×C4—104no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4—101no—
593C22×C4—101no—
594C22×C4—204no—
595C22×C4—204no—
596C22×C4—204no—
597C22×C4—402no—
598C22×C4D4×D512yes—
599C22×C4D4×D511yescharacteristic
600C22×C4C23×D512yes—
601C22×C4C23×D511yescharacteristic
602SD16—108no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—54no—
606C2×C8—52no—
607C2×C8—52no—
608C2×C8—108no—
609C2×C8—108no—
610C2×C8—102no—
611C2×C8C23×D512yes—
612C2×C8C23×D512yes—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—54no—
618C4⋊C4—52no—
619C4⋊C4—52no—
620C4⋊C4—52no—
621C4⋊C4—104no—
622C4⋊C4—104no—
623C4⋊C4—104no—
624C4⋊C4—104no—
625C4⋊C4—104no—
626C4⋊C4—104no—
627C4⋊C4—101no—
628C4⋊C4—101no—
629C4⋊C4—104no—
630C4⋊C4—101no—
631C4⋊C4—104no—
632C4⋊C4C23×D512yes—
633C4⋊C4C23×D512yes—
634C4⋊C4C23×D512yes—
635C22⋊C4—24no—
636C22⋊C4—54no—
637C22⋊C4—54no—
638C22⋊C4—104no—
639C22⋊C4—104no—
640C22⋊C4—104no—
641C22⋊C4—104no—
642C42—52no—
643C42—52no—
644C42—104no—
645C2×C5—24no—
646C2×C5—82no—
647C2×C5#333514yescomplemented
648C2×C5C2×#54711yescharacteristic
649C2×C5C23×SD1611yescharacteristic
650C2×C5C2×#57711yescharacteristic
651D5—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—54no—
659C23—52no—
660C23—102no—
661C23—102no—
662C23D5×SD1614yes—
663C23C2×D4×D512yes—
664C23C2×D4×D511yescharacteristic
665Q8—102no—
666Q8—102no—
667Q8—208no—
668Q8—202no—
669Q8—404no—
670D4—22no—
671D4—22no—
672D4—48no—
673D4—42no—
674D4—516no—
675D4—208no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—54no—
687C2×C4—52no—
688C2×C4—52no—
689C2×C4—52no—
690C2×C4—84no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—104no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—208no—
701C2×C4—208no—
702C2×C4—202no—
703C2×C4—202no—
704C2×C4—208no—
705C2×C4—202no—
706C2×C4—202no—
707C2×C4—404no—
708C2×C4C2×D4×D512yes—
709C2×C4C2×D4×D511yescharacteristic
710C2×C4D5×#4112yes—
711C2×C4#415012yes—
712C2×C4C24×D511yescharacteristic
713C8—22no—
714C8—22no—
715C8—54no—
716C8—102no—
717C5C2×#333511yescharacteristic, complemented, Sylow
718C22—22no—
719C22—28no—
720C22—22no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—54no—
725C22—84no—
726C22—102no—
727C22—108no—
728C22—102no—
729C22#6598912yes—
730C22C2×D5×SD1614yes—
731C22C2×D5×SD1612yes—
732C22#6610912yes—
733C22C22×D4×D511yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—54no—
739C4—102no—
740C4—102no—
741C4—202no—
742C4—202no—
743C4—202no—
744C4—202no—
745C4#6598912yes—
746C4C2×D5×#4111yescharacteristic
747C4C2×#415011yescharacteristic
748C2—24no—
749C2—82no—
750C2—104no—
751C2#1061305114yesdirect product factor
752C2C2×#6598911yescharacteristic
753C2C22×D5×SD1611yescharacteristic
754C2C2×#6610911yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#481C2
socleC23×C5C22×D4
prime radicalC2×#65945C2
hypercenterC2×#481D5
hypocenterC5C2×#3335
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#65845C2semidirect
3. C2×C5×#481C2semidirect
4. C2×#65330C2semidirect
5. C22×#3940C2semidirect
6. #10613051C2direct (N × H)
7. C2×#65143C2semidirect
8. C2×#65151C2semidirect
9. C2×D5×#106C2semidirect
10. C2×#65144C2semidirect
11. C2×#65066C2semidirect
12. C2×#65067C2semidirect
13. C2×#65050C2semidirect
14. C2×#65047C2semidirect
15. C2×#65014C2semidirect
16. C2×#65010C2semidirect
34. #65845C22semidirect
45. C5×#481C22semidirect
59. #65330C22semidirect
66. C2×#3940C22semidirect
67. #65151C22semidirect
68. D5×#106C22semidirect
69. #65144C22semidirect
70. #65143C22semidirect
71. #65067C22semidirect
72. #65066C22semidirect
73. #65050C22semidirect
74. #65047C22semidirect
75. #65014C22semidirect
76. #65010C22semidirect
186. C2×#481D5semidirect
219. C2×C22⋊D5SD16semidirect
288. C2×#168#41semidirect
324. #481C2×D5semidirect
386. C22⋊D5C2×SD16semidirect
416. #168C2×#41semidirect
647. C2×C5#3335semidirect
717. C5C2×#3335semidirect
751. C2#10613051direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#659452
C2×#658452
C2×C5×#4812
C2×#653302
C22×#39402
#106130512
C2×#651432
C2×#651512
C2×D5×#1062
C2×#651442
C2×#650662
C2×#650672
C2×#650502
C2×#650472
C2×#650142
C2×#650102
C2×#33355